1. Field of the Invention
The present invention relates to communication technologies, and more particularly, to a method and device for determining transmit power spectral density (PSD).
2. Background of the Invention
In Digital Subscriber Line (DSL) technology, subscriber cables always contain multiple (25 or more) twisted pair wires. Various services may operate in different twisted pair wires. When Various Subscriber Digital Lines (xDSL) operate simultaneously, crosstalk may occur, which may result in performance loss of some of the lines.
With the boost in the frequency baud that the xDSL technology uses, crosstalk, especially crosstalk in high frequency has become more and more obvious. Because in upstream and downstream directions of the xDSL, frequency division multiplex method is used, near-end crosstalk (NEXT) may not bring too large performance loss, but the far-end crosstalk (FEXT) will bring very large performance loss in the line. If there are multiple lines use XDSL service in a bundle of cables simultaneously, the FEXT may result in that the rates of some of the lines are low, the performance of some of the lines is unsteady, or even some of the lines cannot be activated, etc. As a result, the service penetration rate of the Digital Subscriber Line Access Multiplexer (DSLAM) is low.
In a communication model, there are K users adopting Discrete Multi-tone (DMT) and N sub frequency bands (tones), the signal transmitted in each tone may be separately expressed by:yn=Hnxn+σ  Equation 1
In general, the receiver of each xDSL user regards the interferences from other users, i.e., the crosstalk, as noise. Accordingly, the data rate that the kth user may achieve in the nth sub frequency band, bnk, is given by the Shannon's channel capacity equation:
                              b          n          k                =                              log            2                    (                      1            +                                                            G                  n                  kk                                ⁢                                  S                  n                  k                                                                                                  ∑                                          j                      ≠                      k                                                        ⁢                                                            G                      n                      kj                                        ⁢                                          S                      n                      j                                                                      +                                  σ                  2                                                              )                                    Equation        ⁢                                  ⁢        2            
As can be seen in Equation 2, the crosstalk lowers the transmission capacity of the line badly, in other words, the crosstalk reduces the rate of the line.
Dynamic Spectral Management (DSM) may automatically adjust the transmit PSD of each user in a network for crosstalk Avoidance.
DSM provides spectrum optimization problems as follows.
Spectrum optimization problem I is that the weighted sum of the rates of all users are maximized by adjusting the transmit power of each user in each sub frequency band (tone) subject to that the total power of each user does not exceed a limitation. The mathematic description of this problem is as follows.
                              Maximize          ⁢                                          ⁢                                    ∑                              k                =                1                            K                        ⁢                                                  ⁢                                          ω                k                            ⁢                                                ∑                                      n                    =                    1                                    N                                ⁢                                                                  ⁢                                  b                  n                  k                                                                    ⁢                                  ⁢                              Subject            ⁢                                                  ⁢            to            ⁢                                                  ⁢                          b              n              k                                =                                    log              2                        (                          1              +                                                                    G                    n                    kk                                    ⁢                                      S                    n                    k                                                                                                              ∑                                              j                        ≠                        k                                                              ⁢                                                                  G                        n                        kj                                            ⁢                                              S                        n                        j                                                                              +                                      σ                    2                                                                        )                          ⁢                                  ⁢                                            Subject              ⁢                                                          ⁢              to              ⁢                                                          ⁢                                                ∑                                      n                    =                    1                                    N                                ⁢                                                                  ⁢                                  S                  n                  k                                                      ≤                          P              k                                ,                      ∀            k                          ⁢                                  ⁢                              0            ≤                                          S                n                k                            ⁢                                                          ⁢                              ∀                k                                              ,          n                                    Equation        ⁢                                  ⁢        group        ⁢                                  ⁢        1                            where        Snk is the power allocated for the kth user in the nth sub frequency band;        Gnkk is a transmission coefficient of the kth user in the nth sub frequency band;        Gnkj (j≠k) is a crosstalk coefficient of the jth user to the kth user in the nth sub frequency band;        pk is a limitation on the total power of the kth user;        ωk is a weight coefficient of rate of the kth user;        σ2 is power of noise;        N is the total number of the sub frequency bands;        K is the total number of the users.        
Spectrum optimization problem II is that the rate of a new user, R1, is maximized subject to that the total transmit power of each user does not exceed the limitation and the target rates of the existing users, Rk, k=2, . . . , K, are guaranteed. The mathematic descriptions of this problem are as follows.
                              Maximize          ⁢                                          ⁢                      R            1                          ⁢                                  ⁢                                            subject              ⁢                                                          ⁢              to              ⁢                                                          ⁢                              R                k                                      ≥                          R                              target                ,                k                                              ,                                          ⁢                      k            ≠            1                          ⁢                                  ⁢                              R            1                    =                                    ∑                              n                =                1                            N                        ⁢                          log              (                              1                +                                                                            G                      n                      11                                        ⁢                                          S                      n                      1                                                                                                                          ∑                                                  j                          ≠                          1                                                                    ⁢                                                                        G                          n                                                      1                            ⁢                            j                                                                          ⁢                                                  S                          n                          j                                                                                      +                                          σ                      2                                                                                  )                                      ⁢                                  ⁢                              R            k                    =                                                    ∑                                  n                  =                  1                                N                            ⁢                                                          ⁢                                                log                  (                                      1                    +                                                                                            G                          n                          kk                                                ⁢                                                  S                          n                          k                                                                                                                                                  ∑                                                          j                              ≠                              k                                                                                ⁢                                                                                    G                              n                              kj                                                        ⁢                                                          S                              n                              j                                                                                                      +                                                  σ                          2                                                                                                      )                                ⁢                                                                  ⁢                k                                      ≠            1                          ⁢                                  ⁢                                                            ∑                                  n                  =                  1                                N                            ⁢                                                          ⁢                              S                n                k                                      ≤                          P              k                                ,                      ∀            k                          ⁢                                  ⁢                              0            ≤                                          S                n                k                            ⁢                                                          ⁢                              ∀                k                                              ,          n                                    Equation        ⁢                                  ⁢        group        ⁢                                  ⁢        2                            where        En,ik is transmit power of the kth user in the ith transmission pattern in the nth sub frequency band;        Gnkk is a transmission coefficient of the kth user in the nth sub frequency band;        Rtarget,k is a target rate of the kth user;        Gnkj (j≠k) is a crosstalk coefficient of the jth user to the kth user in the nth sub frequency band;        ponk is transmit PSD of the kth user;        pk is a limitation on the total power of the kth user;        σ2 is power of noise.        
Spectrum optimization problem III is that the minimum rate is maximized (MaxMin) subject to that the total transmit power for each user does not exceed a limitation. The mathematic descriptions of this problem are as follows.
                              maximize          ⁢                                          ⁢                      r            0                          ⁢                                  ⁢                                            subject              ⁢                                                          ⁢              to              ⁢                                                          ⁢                              R                k                                      ≥                          r              0                                ,                                          ⁢                                    R              k                        =                                          ∑                                  n                  =                  1                                N                            ⁢                                                          ⁢                              log                (                                  1                  +                                                                                    G                        n                        kk                                            ⁢                                              S                        n                        k                                                                                                                                      ∑                                                      j                            ≠                            k                                                                          ⁢                                                                              G                            n                            kj                                                    ⁢                                                      S                            n                            j                                                                                              +                                              σ                        2                                                                                            )                                                    ⁢                                  ⁢                                                            ∑                                  n                  =                  1                                N                            ⁢                              S                n                k                                      ≤                          P              k                                ,                      ∀            k                          ⁢                                  ⁢                              0            ≤                                          S                n                k                            ⁢                                                          ⁢                              ∀                k                                              ,          n                                              Equation          ⁢                                          ⁢          group          ⁢                                          ⁢          3                ⁢                                                      where        Snk is the power allocated for the kth user in the nth sub frequency band;        Gnkk is a transmission coefficient of the kth user in the nth sub frequency band;        Gnkj (j≠k) is a crosstalk coefficient of the jth user to the kth user in the nth sub frequency band;        pk is a limitation on the total power of the kth user;        ωk is a weight coefficient of rate of the kth user;        σ2 is power of noise;        Rtarget,k is the target rate of the kth user;        r0 is a minimum of the rates of all the users, that is, r0=min(Rk)        
The above target function with the constrained conditions is all non-convex function. There is no high efficient and complete solution. Among the existing algorithms, the most popular ones are Optimal Spectrum Balancing (OSB) algorithm and Iterative Spectrum Balancing (ISB) algorithm.
In the two algorithms, OSB algorithm is an optimization method and reduces the calculation complexity to O(NeK) under the premise that the optimized solution is searched exhaustively. In the case that the number of users, K, is not too large, the result of the calculation may be acquired in an acceptable time. However, if the number of users increases, the calculation time increases in an exponential manner and increases to an unacceptable extent very soon.
The ISB algorithm is an improved algorithm on the basis of the OSB and reduces the calculation complexity to O(NK2).
The calculation complexity of the DSM algorithm is still in a high level although complexity reduction is given by the above two methods. When a transmit spectrum and transmit PSD are determined on the basis of the above two algorithms, too much time are used. The transmission efficiency is low.